Problem 4
Seventeen people correspond by mail with one another, each with all the rest. In their letters only three different topics are discussed, and each pair of correspondents deals with only one topic. Prove that at least three people write to each other about the same topic.
Step 2 of 5: Finish the lemma
Detailed analysis
If any edge among is red, it forms a red triangle with . If none is red, all three edges among them have the other color and form a triangle of that color.